To avoid this problem and allow general usage, we propose to leverage RNN methods to compute the learnable terms \(\Delta {\mathbf {\gamma }}\) , \(\Delta {\mathbf {\beta }}\) , and \(\Delta {\mathbf {q}}\)  instead of the relative poses. As analyzed previously, all those terms are functions of the motion dynamic terms \(^{I}\mathbf {\omega }\)  and \(^{I}\mathbf {a}\)  only, and independent of prior information on local gravity direction, local velocity term, and so on. Since \(^{I}\mathbf {\omega }\)  and \(^{I}\mathbf {a}\)  are both measured by the IMU sensor, our method directly captures the intrinsic model of an IMU. By contrast, the network in previous methods [1]}, [2]}, [3]} express both IMU models and motion patterns in the training datasets.
Our design also aligns well with the closed-form solutions that
use \(\Delta {\mathbf {\gamma }}\) , \(\Delta {\mathbf {\beta }}\) , and \(\Delta {\mathbf {q}}\)  for later sensor fusion [4]}, [5]}.
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